In a medium the speed of light wave decreases to $0.2$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $x: 1$. The value of $x$ is _________.
(Given speed of light in free space $=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$ and for the given medium $\mu_{\mathrm{r}}=1$)
Answer (integer)
5
Solution
We know that $v=\frac{c}{n}=\frac{c}{\sqrt{\varepsilon_{r}}}$
<br/><br/>Putting the values:
<br/><br/>$0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}$
<br/><br/>$\Rightarrow \sqrt{\varepsilon_{r}}=5$
<br/><br/>$\Rightarrow$ Required ratio $=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5$
<br/><br/>$\Rightarrow x=5$
About this question
Subject: Physics · Chapter: Electromagnetic Waves · Topic: Properties of EM Waves
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